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研究所、轉學考(插大)-微積分
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109年 - 109 國立高雄師範大學轉學生招生考試試題_電機工程學系二年級：微積分#116352
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題組內容
4. For the curve y
2
+ 2x
2
y − x
4
= 7,
(b) find the slope of the tangent line to the curve at the point (1, 2). (5%)
其他申論題
(a) Find . (5%)
#496828
(b) Show that ax = ax ln(a). (5%)
#496829
3. Find the relative extrema of the function f(x) = x3 + 3x2 − 9x − 13. (10%)
#496830
(a) find ; (5%)
#496831
(a) ∫ 16x3 ln(x) dx (5%)
#496833
(b)cos(2x) sin(4x +π/4)dx (5%)
#496834
6. Evaluatedt. (10%)
#496835
7. Evaluateydx, where x = 2t − 1 and y = t2 + 2. (10%)
#496836
8. Evaluate dA over the region ?? in the first quadrant bounded by the graphs of y = x2, x = 0, y = 4 (see Fig.1). (10%)
#496837
9. Evaluate dxdy reversing the order of integration. (Hint: Draw the integration area first.) (10%)
#496838
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